Ricciardo suffered an engine power problem early in the race, with even his team fearing he would have to retire within a couple of laps, but the Australian somehow held on to win F1's jewel in the crown for the first time.
Ricciardo led the race right from the green lights with Vettel holding on to second, while Hamilton, Raikkonen and Bottas following closely.
There is a phase of that race I'm really not proud of.
When Verstappen threw away victory back in China whilst running into Vettel, I mistakenly thought it would be the turning point for him to begin to play the percentages better and choose his battles more carefully.
He added: "I spoke to Prince Albert the other day and said maybe we should make it longer". The Australian driver was left to complete the race with just his internal combustion engine.
With an average of 809,000 people watching, the telecast was the most-viewed Formula 1 race on cable since the 1995 Italian Grand Prix, which also aired on ESPN and averaged 876,000 viewers.
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"We set a statement on Thursday, we've been quickest in every session and we've just got the race tomorrow and then we'll celebrate", said Ricciardo. "I'm stoked. There were a few doubts that came in mid-race, but we've won Monaco - feels good, feels good". It's also a race where it's extremely hard to overtake, which Vettel was reminded of as he trailed Ricciardo for half the race.
"It was a bit boring, the race", said Vettel. While the Hyper was mighty in qualifying to generate a sub-71 second lap on the two mile series of corners, none of the compounds turned into a proper race tyre. Daniel had the answers at all times. Sergey Sirotkin showed impressive pace in the struggling Williams throughout practice and qualifying and will start 13th ahead of Charles Leclerc, who qualified his Sauber in 14th at the first home grand prix of his career. At the restart I didn't have much confidence in the tyres, I lost quite a lot.
Hamilton has won the past two races and leads the championship by 17 points ahead of Vettel, who won the opening two races.
Daniel Ricciardo is out of contract with Red Bull at the end of the season and is yet to sign a new deal, leading to suggestions he could switch teams. He immediately fell into the clutches of Vettel, who went into full-on attack mode.
In the early part of the race, several drivers radioed their team pit-walls complaining about the slow pace of the race. It was yet another mistake from the Kiwi in what is becoming a run of missed opportunities for the Le Mans victor. McLaren's Fernando Alonso also failed to finish for the first time this season after smoke started to emerge from his vehicle on lap 53.